Can I read Inner Product Spaces on EtoBox?

Inner Product Spaces by Sheldon Jay Axler is a book available to read on EtoBox.

What is Inner Product Spaces about?

In making the definition of a vector space, we generalized the linear structure (addition and scalar multiplication) of R 2 and R 3 . We ignored geometric features such as the notions of length and angle. These ideas are embedded in the concept of inner products, which we will investigate in this chapter. Every inner product induces a norm, which you can think of as a length. This norm satisfies key properties such as the Pythagorean theorem, the triangle inequality, the parallelogram equality, and the Cauchy-Schwarz inequality. The notion of perpendicular vectors in Euclidean geometry gets renamed to orthogonal vectors in the context of an inner product space. We will see that orthonormal bases are tremendously useful in inner product spaces. The Gram-Schmidt procedure constructs such bases. This chapter will conclude by putting together these tools to solve minimization problems.

Author

Sheldon Jay Axler

Publisher

Springer International Publishing : Imprint: Springer

Published

2023

Language

EN

ISBN

9783031410260

Subjects

Mathematics, Stem